On the Fejér means of bounded Ciesielski systems

• Autorzy: Ferenc Weisz
• Języki publikacji: EN

Abstrakty

EN

We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space $H_{p}$ to $L_{p}$ if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n → ∞.

Kategorie tematyczne

• 46B15: Summability and bases
• 41A15: Spline approximation
• 42B08: Summability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 146
• Numer: 3
• Strony: 227-243

Daty

wydano

2001

Twórcy

autor

Ferenc Weisz

• Department of Numerical Analysis, Eötvös L. University, Pázmány P. sétány 1/D, H-1117 Budapest, Hungary

Identyfikatory

DOI

10.4064/sm146-3-2